
Mathematical Thought and its Objects
Charles Parsons(Author)
Cambridge University Press
Published on 24. December 2007
Book
Hardback
400 pages
978-0-521-45279-3 (ISBN)
Description
Charles Parsons examines the notion of object, with the aim to navigate between nominalism, denying that distinctively mathematical objects exist, and forms of Platonism that postulate a transcendent realm of such objects. He introduces the central mathematical notion of structure and defends a version of the structuralist view of mathematical objects, according to which their existence is relative to a structure and they have no more of a 'nature' than that confers on them. Parsons also analyzes the concept of intuition and presents a conception of it distantly inspired by that of Kant, which describes a basic kind of access to abstract objects and an element of a first conception of the infinite.
Reviews / Votes
'This complete presentation of structuralism as a foundation programme in the philosophy of mathematics enriches significantly the debate and anyone interested in this area of studies will need to consider its relevance.' Minds & MachinesMore details
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 28 mm
Weight
798 gr
ISBN-13
978-0-521-45279-3 (9780521452793)
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Schweitzer Classification
Other editions
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Charles Parsons
Mathematical Thought and its Objects
Book
09/2009
Cambridge University Press
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Charles Parsons
Mathematical Thought and its Objects
E-Book
03/2008
1st Edition
Cambridge University Press
€44.49
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Person
Charles Parsons holds an AB (mathematics) and PhD (philosophy) from Harvard University and studied for a year at King's College, Cambridge. He was on the faculty at Harvard University from 1962-5 and 1989-2005 and at Columbia University from 1965-89. His publications are mainly in logic, philosophy of mathematics, and Kant. He was an editor of the posthumous works of Kurt Goedel (Collected Works, Volumes III-V).
Author
Edgar Pierce Professor of Philosophy, EmeritusHarvard University, Massachusetts
Content
Preface; 1. Objects and logic; 2. Structuralism and nominalism; 3. Modality and structuralism; 4. A problem about sets; 5. Intuition; 6. Numbers as objects; 7. Intuitive arithmetic and its limits; 8. Mathematical induction; 9. Reason.